Math451 Unit 2 Questions Allocation
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Colorado Technical University *
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451
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Mathematics
Date
Feb 20, 2024
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docx
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Uploaded by JudgeKnowledgeCheetah31
Math451
Unit 2 Allocation
Questions
Helen’s transportation company tries to deliver the following crops with two identical trucks. There are a total of 600 boxes of apples, 500 boxes of bananas, 450 boxes of nectarines, and 350 boxes of peaches. These equal sized boxes can carry up to 25 pounds of apples, 35 pounds of bananas, 45 pounds of nectarines, and 30 pounds of peaches. The shipping charge for apples, bananas, nectarines, and peaches are $6.35, $6.45, $6.35, and $6.50 per box, respectively. Each truck has a weight limit of 32,000 pounds and a capacity not more than 1,000 boxes.
Question 1
How much is the capacity of Truck #2 completely loaded and is ready to move?
1,000 boxes
900 boxes
100 boxes
32,000 boxes
Solution
The correct answer is:
1,000 boxes
Correct
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Question 2
What crop was completely loaded to Truck #1?
Peaches and nectarines
Apples and peaches
Bananas
Peaches
Solution
The correct answer is:
Peaches
Correct
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Question 3
What is the value for the objective function after running the problem through Excel’s Solver?
$12,167.50
$1,000
$32,000
$7,722.50
Solution
The correct answer is:
$12,167.50
Correct
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Question 4
What resources does Helen run out first in delivering the crops?
Weight and capacity of Truck #2
None
Weight and capacity of Truck #1
Weights of both trucks
Solution
The correct answer is:
None
Correct
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Question 5
Which of the following crops did she completely deliver after running the problem through Excel’s Solver?
Bananas, nectarines, and peaches
All of the crops
Apples, bananas, and peaches
Apples, bananas, and nectarines
Solution
The correct answer is:
All of the crops
Correct
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Question 6
Abstraction helps focus on some parts of the problem by hiding certain details.
Consider a trucking company that is delivering the following crops:
500 boxes of apples, 25 pounds each
450 boxes of bananas, 35 pounds each
400 boxes of nectarines, 45 pounds each
400 boxes of peaches, 30 pounds each
The shipping charge for apples, bananas, nectarines, and peaches are $6.10,
$6.35, $6.20, and $6.40 per box, respectively. The truck has a weight limit of
35,000 pounds and a capacity of no more than 1,100 boxes. The goal is to maximize the total shipping charge.
Using the trucking problem above, there are products
and weights per product
. There is a weight limit WL.
Which of the following expresses the weight limit? Let
be the number of
that is shipped.
Solution
The correct answer is
Correct
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Question 7
Consider a trucking company that is delivering the following crops:
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500 boxes of apples, 25 pounds each
450 boxes of bananas, 35 pounds each
400 boxes of nectarines, 45 pounds each
400 boxes of peaches, 30 pounds each
The shipping charge for apples, bananas, nectarines, and peaches are $6.10,
$6.35, $6.20, and $6.40 per box, respectively. The truck has a weight limit of
35,000 pounds and a capacity of no more than 1,100 boxes. The goal is to maximize the total shipping charge.
The trucking problem above features several different limits.
Modify the problem slightly using the following information:
Product
Weight
Value
Number
Apple
25
6.1
600
Banana
35
6.35
500
Nectarine
45
6.2
550
Peach
30
6.55
650
The limits are at most 1,200 products and a maximum weight of 40,000. What is the maximum shipment value?
$7,606.50
$8,049.00
$8,639.00
$7,742.50
Solution
The correct answer is
$7,742.50
Correct
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Question 8
Consider a trucking company that is delivering the following crops:
500 boxes of apples, 25 pounds each
450 boxes of bananas, 35 pounds each
400 boxes of nectarines, 45 pounds each
400 boxes of peaches, 30 pounds each
The shipping charge for apples, bananas, nectarines, and peaches are $6.10,
$6.35, $6.20, and $6.40 per box, respectively. The truck has a weight limit of
35,000 pounds and a capacity of no more than 1,100 boxes. The goal is to maximize the total shipping charge.
What happens if you add a fourth small truck to the trucking problem above?
Modify the problem slightly using the following information.
Product
Weight
Value
Number
Apple
25
6.1
600
Banana
35
6.35
500
Nectarine
45
6.2
550
Peach
30
6.55
650
Suppose that instead of one big truck, you have four smaller ones, each with a weight limit of 20,000 and a package limit of 900. Set this up with variables
for the number of boxes shipped for each truck. This will give you 16 decision
variables. You will need to constrain the total number shipped, as well as the weight and number of boxes per truck. Use the simplex method.
Which fruit will be shipped on several different trucks?
Nectarine
Just apple and banana
Banana
All four
Solution
The correct answer is
Nectarine
Correct
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